Blender: morphing object shape
Select both objects then in the mesh properties under ShapeKeys you will find an option to "Join as Shapes" in the menu under the add/remove buttons. This makes a shapekey in the active object that matches the other object.

With the shapekey selected in the list you can animate the value to morph between the two shapes. Either press I while the mouse is over the value or right-click and select Insert Keyframe.